Is it possible to use timeline markers for driver expression?
It is possible to use marker for rendering frame ranges, but not through driver, which is normally used to trigger value change based on Scene.frame_current. What you need instead, is property manipulation based on TimeLineMarker.frame.

The only thing you need to do is iterating over Scene.timeline_markers, because manipulation of Scene.frame_start and Scene.frame_end for each render batch is already taken care of by the addon. Get the list of frame ranges used by the addon, which is Scene.batch_render.frame_ranges, and insert positions of the pair of markers into it. It is this last step that wouldn't be made simpler by a driver.

Below's an operator for you to edit and use. It converts each pair of markers named start and end directly into frame ranges:

class OBJECT_OT_MarkerToFrameRanges(bpy.types.Operator):
    bl_idname = "batch_render.marker_to_frame_ranges"
    bl_label = "Marker To Frame Ranges"

    def execute(self, context):
        batcher = context.scene.batch_render
        marker_list = sorted(context.scene.timeline_markers,
                             key=lambda x: x.frame)
        marker_frame_ranges = []

        for marker in marker_list:
            if marker.name == 'start':
                marker_frame_ranges.append({'start': marker.frame})
            elif marker.name == 'end':
                range_dict = marker_frame_ranges[-1] if marker_frame_ranges\
                    else {}                
                range_dict['end'] = marker.frame

        for index, range_dict in enumerate(marker_frame_ranges):
            marker_start = range_dict.get('start', 0)
            marker_end = range_dict.get('end', context.scene.frame_end)

            if index &gt;= len(batcher.frame_ranges):
                bpy.ops.batch_render.add_new()

            batcher.frame_ranges[index].start_frame = marker_start
            batcher.frame_ranges[index].end_frame = marker_end

        return {'FINISHED'}


EDIT: To strictly answer your question: Yes, it is possible to use timeline marker for driver expression. The function below will return True only if there's a marker at the current frame:

def any_marker_at_frame():
    frame_current = bpy.context.scene.frame_current
    markers = bpy.context.scene.timeline_markers

    for m in markers:
        if m.frame == frame_current:
            return True
    return False

bpy.app.driver_namespace['any_marker_at_frame'] = any_marker_at_frame


You can then use any_marker_at_frame() in your scripted expression.